1. Field of the Invention
This invention relates to computation, and more specifically to quantum cryptography and quantum computing.
2. Discussion of the Background
Quantum mechanical systems have been investigated for many applications including quantum cryptography and quantum computation. Information may be stored and processed in such a quantum system. Often the information is carried by two-state quantum subsystems. Each two-state quantum subsystem is called a quantum bit (“qubit”). Such quantum mechanical processing systems may outperform classical computers in such tasks as prime factorization problems.
Physical implementations of qubits have the problem that the quantum system which carries the information are coupled to the environment. This leads to a process known as decoherence in which encoded quantum information is lost to the environment. U.S. Pat. No. 6,128,764 to Gottesman discusses quantum cryptography and quantum computation.
In order to remedy this problem, active quantum error-correcting codes (QECCs) have been developed in analogy with classical error correction. These codes encode quantum information over an entangled set of code words the structure of which serves to preserve the quantum information when frequent measurements of the errors and correction of any resulting errors are done.
One major development in the formulation of QECC has been the advent of stabilizer code theory. In this formalism, a set of stabilizer operators is defined, and the code is the common eigenspace of the stabilizer elements with eigenvalue +1.
The decoherence-free subsystem (DFS) approach is another method that has been developed to combat decoherence resulting from a specific decoherence mechanism. In contrast to the active mode of QECC, the DFS approach utilizes the symmetry of the system-environment coupling to find a subspace of the system which does not experience decoherence. The quantum information the user wishes to encode in the system is expressed by means of states contained in the decoherence-free subsystem.
The inventors recognized that, from the perspective of quantum computation, it is also important to be able to controllably transform decoherence-protected states. Once the information encoded in the quantum system has been protected from decoherence by some method such as a DFS, it is useful to be able to perform universal quantum computation. The idea of universal computation is the following: with a restricted set of operations called a universal set, one wishes to implement any unitary transformation on the given Hilbert space to an arbitrary degree of accuracy. There are a number of universal sets that have been identified.